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Huemer’s Paper on Simplicity

Mike’s paper on simplicity, noted in the comments of his post on the topic is now available here. I didn’t want the paper to get lost at the end of a long series of comments, so I’m moving the notice here and linking to it in the sidebar under Works in Progress.

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Huemer’s Paper on Simplicity — 3 Comments

Ok, here’s the question (for those who lack the time to read that long paper):
Can anyone tell me why simplicity should be a virtue of philosophical theories in particular? (The suggestions in the simplicity thread seemed to all address scientific theories.)

For example, David Lewis says modal realism is good because it reduces the number of primitive concepts we have to accept (and, presumably, the number of irreducible phenomena). We get to reduce propositions, properties, etc., if we just admit possible worlds and sets. Question: How is this a reason for believing modal realism?

Your paper looks interesting, though I haven’t had time to read it carefully yet. I will take a stab at your question about the appeal to simplicity in philosophy. I’m not sure there is anything here you haven’t already considered (since I’m sympathetic with what I take to be your main view, which is skepticism about the use if parsimony (simplicity) in philosophy).

The way I always understood Lewis appeal to simplicity is by understanding the way that Quine appeals to simplicity. Lewis was a student of Quine’s, and despite their many differences, I think he shares a basic outlook with Quine about simplicity. In particular, Quine famously thinks (in 2 Dogs and elsewhere) that the way in which you get to conclude that electrons or sets or whatever exist is that they are an indispensable part of your best overall explanatory picture of the world — and the best picture is the one that accounts for the “data” (observations /”the passing show” as Quine calls it in Word and Object) in a way that is the most explanatory and is “simplest” in some sense.

Now, Quine, I suspect, thinks that the appeal to simplicity is justified because scientists, he thinks, legitimately appeal to simplicity as an epistemic virtue, and so — since philosophy is in some way just continuous with science (rejection of A/S distinction, etc.) presto — you get a justification for the use of simplicity in philosophy, too. If, for some reason, Quine thought that science didn’t justify the appeal to simplicity, I think he’d be suspicious about its use in philosophy. But, he would say, just look at great scientists like Newton and Einstein who made appeal to simplicity as (apparently) an epistemic virtue.

I think Lewis inherits part of this picture, even if he isn’t always very explicit about it. The way you figure out what exists is by looking at your best “most explanatory” and simplest picture of the world that is also the most fruitful in resolving various puzzles and explaining stuff.

Now, suppose this (no doubt simplified) idea is right, vague though it is. Two points:

(1) My view is that a careful examination of the use of simplicity in science shows that there is no general methodological justification for it. Philosophers who think about confirmation have largely come around to this view, for example. Think about the failure to generate content independent rules of inductive logic analogous to deductive rules (e.g., the grue problem highlights some of the difficulties here). Scientists like Newton thought that appeal to parsimony was justified because he thought God made the Universe simple. But absent this sort of justification, and absent a purely methodological one, it looks like the only justifications for legitimate, epistemic appeals to parsimony are based on local empirical claims, where one has some empirical evidence that there is something simple about the process in question). If this is right, then philosophers can no longer rely on science to justify their appeal to simplicity, since philosophical use of simplicity, if it is to respect the scientific model, won’t be able to distinguish between predictively or empirically equivalent alternatives, and those are (often? Usually? Always?) precisely the kind of cases where philosophers want to make use of simplicity.

(2) Of course, one might think that there are other ways to justify simplicity without appealing to its use in science. Perhaps there is some purely philosophical methodology that will do the trick. I am skeptical that there is such a purely philosophical justification (and I guess Michael is too). It would be neat if someone could provide one. But I suspect (and this is only a suspicion) that most philosophical use of simplicity has depended on one of two routes: either the God route (assumptions about the world being simple), or the science route (a purely methodological justification that is supposed to be modeled off of its use in science). Neither option looks promising.

I guess I’m just offering a (rather) speculative diagnosis here, rather than answering your question. Like you (Michael), I’d like to know if there are any other ways philosophers have tried to justify parsimony. I’d also be interested in whether anyone thinks my speculations about Lewis are plausible. Does he say somewhere explicitly why he thinks appeal to simplicity is legit?

People like to quote Lewis’ remark to the effect that only qualitative simplicity (reduction in the number of distinct kinds) and not quantitative simplicity (reduction in the number of instances of a kind) matters. But Lewis provided no justification for this. Likewise, the philosophical appeals to simplicity that I am familiar with come with no justification or explanation. (I’m thinking of, e.g., Smart and Churchland on physicalism vs. dualism; Quine on nominalism vs. platonism; and analytic metaphysicians such as Lewis.)

If philosophical simplicity isn’t valuable for the reason, or in the way, that simplicity of scientific theories is, then I think there’s no reason to think it is valuable at all.

As to the scientific route: I’m more friendly to general defenses of simplicity in science than you are. One approach is Jeffreys’, in which you have to assign ever decreasing probabilities to higher possible degrees of complexity in order to have your probabilities sum to 1 (because there are infinitely many degrees of complexity). Another is the Bayesian likelihoods approach, according to which simpler models tend to be compatible with fewer possible sets of data; as a result, for those few sets of data that they are compatible with, they have much higher likelihoods.

But neither of these approaches works well for philosophical theories. The first doesn’t work well, because competing philosophical theories generally do not belong to infinite sets of theories; there are usually only two or three salient alternatives, with no reason for assigning a higher a priori probability to one of them than the others (without looking at specific philosophical arguments for one or another theory).

The second approach doesn’t work well, because it is not generally clear that simple *philosophical* theories are compatible with a narrower range of data than their more complex rivals. For example, it is unclear in what way nominalism might be compatible with a narrower range of data than platonism.